On spectra of unitary Cayley mixed graph
Chandrashekar
Adiga
University of Mysore
author
B. R.
Rakshith
University of Mysore
author
text
article
2016
eng
In this paper we introduce mixed unitary Cayley graph $M_{n}$ $(n>1)$ and compute its eigenvalues. We also compute the energy of $M_{n}$ for some $n$.
Transactions on Combinatorics
University of Isfahan
2251-8657
5
v.
2
no.
2016
1
9
http://toc.ui.ac.ir/article_10169_a755cdbb319870a9ab31c2f06938b219.pdf
dx.doi.org/10.22108/toc.2016.10169
Recursive construction of $(J,L)$ QC LDPC codes with girth 6
Mohammad
Gholami
Shahrekord University
author
Zahra
Rahimi
University of Shahrekord,
author
text
article
2016
eng
In this paper, a recursive algorithm is presented to generate some exponent matrices which correspond to Tanner graphs with girth at least 6. For a $J \times L$ exponent matrix $E$, the lower bound $Q(E)$ is obtained explicitly such that $(J,L)$ QC LDPC codes with girth at least 6 exist for any circulant permutation matrix (CPM) size $m \geq Q(E)$. The results show that the exponent matrices constructed with our recursive algorithm have smaller lower-bound than the ones proposed recently with girth 6.
Transactions on Combinatorics
University of Isfahan
2251-8657
5
v.
2
no.
2016
11
22
http://toc.ui.ac.ir/article_8430_4d65fe9a28acc359f137574e8342c0f4.pdf
dx.doi.org/10.22108/toc.2016.8430
Degree distance and Gutman index of increasing trees
Ramin
Kazemi
Department of statistics, Imam Khomeini International University, Qazvin
author
Leila
Meimondari
Imam Khomeini International University
author
text
article
2016
eng
The Gutman index and degree distance of a connected graph $G$ are defined as \begin{eqnarray*} \textrm{Gut}(G)=\sum_{\{u,v\}\subseteq V(G)}d(u)d(v)d_G(u,v), \end{eqnarray*} and \begin{eqnarray*} DD(G)=\sum_{\{u,v\}\subseteq V(G)}(d(u)+d(v))d_G(u,v), \end{eqnarray*} respectively, where $d(u)$ is the degree of vertex $u$ and $d_G(u,v)$ is the distance between vertices $u$ and $v$. In this paper, through a recurrence equation for the Wiener index, we study the first two moments of the Gutman index and degree distance of increasing trees.
Transactions on Combinatorics
University of Isfahan
2251-8657
5
v.
2
no.
2016
23
31
http://toc.ui.ac.ir/article_9915_00377372a764b119bb3640a24a194a64.pdf
dx.doi.org/10.22108/toc.2016.9915
On the number of connected components of divisibility graph for certain simple groups
Adeleh
Abdolghafourian
Yazd University
author
Mohammad Ali
Iranmanesh
Yazd University
author
text
article
2016
eng
The divisibility graph $\mathscr{D}(G)$ for a finite group $G$ is a graph with vertex set $cs(G)\setminus\{1\}$ where $cs(G)$ is the set of conjugacy class sizes of $G$. Two vertices $a$ and $b$ are adjacent whenever $a$ divides $b$ or $b$ divides $a$. In this paper we will find the number of connected components of $\mathscr{D}(G)$ where $G$ is a simple Zassenhaus group or an sporadic simple group.
Transactions on Combinatorics
University of Isfahan
2251-8657
5
v.
2
no.
2016
33
40
http://toc.ui.ac.ir/article_8595_8e231b4595dc014a92b1ce8c12a9732f.pdf
dx.doi.org/10.22108/toc.2016.8595
On the spectrum of $r$-orthogonal Latin squares of different orders
Hanieh
Amjadi
Alzahra University
author
Nasrin
Soltankhah
Alzahra University
author
Naji
Shajarisales
Max Planck Institute for Intelligent Systems
author
Mehrdad
Tahvilian
Sharif University of Technology
author
text
article
2016
eng
Two Latin squares of order $n$ are orthogonal if in their superposition, each of the $n^{2}$ ordered pairs of symbols occurs exactly once. Colbourn, Zhang and Zhu, in a series of papers, determined the integers $r$ for which there exist a pair of Latin squares of order $n$ having exactly $r$ different ordered pairs in their superposition. Dukes and Howell defined the same problem for Latin squares of different orders $n$ and $n+k$. They obtained a non-trivial lower bound for $r$ and solved the problem for $k \geq \frac{2n}{3} $. Here for $k < \frac{2n}{3}$, some constructions are shown to realize many values of $r$ and for small cases $(3\leq n \leq 6)$, the problem has been solved.
Transactions on Combinatorics
University of Isfahan
2251-8657
5
v.
2
no.
2016
41
51
http://toc.ui.ac.ir/article_11665_93148cb85b3fdaf4b4abfe8412331040.pdf
dx.doi.org/10.22108/toc.2016.11665